Mechanical design engineers who have to build or modify a machine are often concerned with designing the time diagram of the related movements between each part of the machine. The timing diagram is a useful tool for the designer not only to see how each part of the machine works together, but also to see the opportunity to improve machine motion through “overlapping” motion. If we design the timing diagram using the old robot style as seen in the movies, it will waste time waiting for another part to finish its move first. If we think about the movement of the human hand when transferring the object, we will see that it will not act like the robot. We can see some overlays. For example, if we transfer a reed from the right hand to the left, we will see that the left hand already closes a little when the right hand moves the reed to the left. The left hand will not open very much and will wait until the bar reaches it and then it will close, because it is not natural. If we use the same approach to design the timing diagram of the machine, we will get smoother movement of the relevant parts.

**Why does the overlap movement provide a smoother movement of the parts? **

Suppose we use a cycloidal cam profile to move the part. So we first have to get the formula to calculate the maximum acceleration of the cycloid cam profile. If the speed of the machine is **NOT** (pcs / h) and the indexing angle (degrees) is **Bm,** indexing time (second) **tm **can be calculated as follows.

Cycle time (sec) = 3600 / N

Indexing time tm (sec) = (Bm / 360) x Cycle time = (Bm / 360) x (3600 / N)

Therefore, the indexing time tm (sec) = 10Bm / N

The profile of the cycloidal motion cam has the following displacement equation.

h = hm x [t/tm- 1/(2 x 3.141592654) x sin(2 x 3.141592654 x t/tm)]

where: hm = Maximum displacement (m) and tm = Indexing time (s)

We can obtain the speed equation by differentiation.

v = dh / dt = hm x [1/tm – (2 x 3.141592654)/(2 x 3.141592654 x tm) x cos(2 x 3.141592654 x t/tm)]

v = hm / tm x [1 – cos(2 x 3.141592654 x t/tm)]

So the acceleration is as follows.

a = dv / dt = hm / tm x [0 – (-2 x 3.141592654/tm) x sin(2 x 3.141592654 x t/tm)]

a = 2 x 3.141592654 x hm / tm ^ 2 x sin (2 x 3.141592654 xt / tm)

Maximum acceleration (amplitude) occurs when sin (2 x 3.141592654 xt / tm) = 1 or -1. Therefore, the amplitude of maximum acceleration is as follows. **amax = 2 x 3.141592654 x hm / tm ^ 2**

We can clearly see from the above derivations that the acceleration is inversely proportional to the square of the indexing time. Since the indexing time ™ is proportional to the indexing angle (Bm), then **the maximum acceleration is also inversely proportional to the square of the indexing angle**. **That means if we can increase the indexing angle by a factor of two, the maximum acceleration will be reduced by a factor of four!** And we can do this by putting more overlap motion into the timing diagram layout. Read more details on how to design a smarter timing diagram at http://mechanical-design-handbook.blogspot.com/.